Sign In Start Free Trial
Account

Add to playlist

Create a Playlist

Modal Close icon
You need to login to use this feature.
  • Book Overview & Buying A Handbook of Mathematical Models with Python
  • Table Of Contents Toc
  • Feedback & Rating feedback
A Handbook of Mathematical Models with Python

A Handbook of Mathematical Models with Python

By : Ranja Sarkar, Dr. Ranja Sarkar
4.1 (7)
close
close
A Handbook of Mathematical Models with Python

A Handbook of Mathematical Models with Python

4.1 (7)
By: Ranja Sarkar, Dr. Ranja Sarkar

Overview of this book

Mathematical modeling is the art of transforming a business problem into a well-defined mathematical formulation. Its emphasis on interpretability is particularly crucial when deploying a model to support high-stake decisions in sensitive sectors like pharmaceuticals and healthcare. Through this book, you’ll gain a firm grasp of the foundational mathematics underpinning various machine learning algorithms. Equipped with this knowledge, you can modify algorithms to suit your business problem. Starting with the basic theory and concepts of mathematical modeling, you’ll explore an array of mathematical tools that will empower you to extract insights and understand the data better, which in turn will aid in making optimal, data-driven decisions. The book allows you to explore mathematical optimization and its wide range of applications, and concludes by highlighting the synergetic value derived from blending mathematical models with machine learning. Ultimately, you’ll be able to apply everything you’ve learned to choose the most fitting methodologies for the business problems you encounter.
Table of Contents (16 chapters)
close
close
1
Part 1:Mathematical Modeling
4
Part 2:Mathematical Tools
11
Part 3:Mathematical Optimization

Filtration of measurements

The Kalman filter has inputs and outputs like any filter. The inputs are noisy and inaccurate measurements, while the outputs are much less noisy and more accurate estimates. Mathematically speaking, the inputs to the filter are a measured value and measurement covariance matrix. The dynamic system model is the state transition matrix (representing equations) and process noise covariance matrix, the Kalman gain is internal and dependent on the system, and the outputs from the filter are the state variable and state covariance matrix. This is illustrated in Figure 7.4a:

Figure 7.4a: Input and output of the Kalman filter

Figure 7.4a: Input and output of the Kalman filter

When an estimate is propagated in time, the future state is inherently uncertain and hence, the error covariance matrix grows with time. The dynamic model (equations of motion) is approximate; the process noise (uncertainty) adds to the existing noise, and this is represented by the process noise covariance matrix...

Unlock full access

Continue reading for free

A Packt free trial gives you instant online access to our library of over 7000 practical eBooks and videos, constantly updated with the latest in tech
bookmark search playlist download font-size

Change the font size

margin-width

Change margin width

day-mode

Change background colour

Close icon Search
Country selected

Close icon Your notes and bookmarks

Delete Bookmark

Modal Close icon
Are you sure you want to delete it?
Cancel
Yes, Delete

Confirmation

Modal Close icon
claim successful

Buy this book with your credits?

Modal Close icon
Are you sure you want to buy this book with one of your credits?
Close
YES, BUY